Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

The daily mass of peaches sold in a supermarket follows a normal distribution with mean $65.8\text{ kg}$ and standard deviation $9.6\text{ kg}$.
(a)[3]

Find the probability that the mass of peaches sold on a chosen day lies between $56\text{ kg}$ and $75\text{ kg}$.

(b)[3]

Find $\sigma$.

(c)[1]

Find the probability that, in a randomly selected week, the first day on which less than $59.1\text{ kg}$ of cherries are sold is the fifth day of the week.

(d)[2]

Find the probability that, in a randomly selected week, the first day on which less than $59.1\text{ kg}$ of cherries are sold comes before the fifth day of the week.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Standardisation shown correctly $\frac{56-65.8}{9.6}<Z<\frac{75-65.8}{9.6}$.

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